STACK. 
ANNEX 


SIMPLIFIED 
MECHANICAL  PERSPECTIVE 


FREDERICK 


SIMPLIFIED 


FOR   THE   USE  OK 


HIGH  SCHOOLS,  .TECHNICAL  AND  MANUAL  TRAINING 

HIGH  SCHOOLS,  EVENING  INDUSTRIAL 

SCHOOLS  AND  ART  SCHOOLS 


BY 

FRANK  FORREST  FREDERICK 

Director  of  Trenton  School  of  Industrial  Arts:  Author  of      Plaster  Casts  and 

How  They  are  Made",  "The  Wash  Method  of  Handling 

Water  Colour",  Etc. 


THE  MANUAL  ARTS  PRESS 

PEORIA,    ILLINOIS 


COPYRIGHT 

FRANK  FORREST  FREDERICK 
1908-  1W) 


CONTENTS 

AUTHOR'S  NOTE 5 

INTRODUCTION 7 

THK  PERSPECTIVE  DIAGRAM 9 

To  Lay  Out   Diagram 11 

To  Find  Vanishing   Points 11 

Problems  I  to  XII 13 

THK  PERSPECTIVE  OF  FURNITURE  AND  INTERIORS 24 

Problems  XIII  to  XX 24 

THE  PERSPECTIVE  OK  CIRCLES 37 

Problems  XXI  to  XXIX 37 

THE  PERSPECTIVE  OF  OBLIQUE  LINES 46 

Problems  XXX  to  XXXVII  ..  .49 


2066125 


AUTHOR'S  NOTE. 

IN  publishing  the  following  notes  on  perspective 
which,  in  substantially  their  present  form,  I 
have  used  with  classes  for  more  than  twenty 
years,  I  wish  to  say  that  I  never  had  a  student  who 
learned  much  about  the  subject  unless  he  carefully 
worked  each  problem  and  thoroughly  understood  it 
before  attempting  the  next;  nor  do  I  believe  anyone 
can  get  much  benefit  from  this  series  of  problems 
without  following  the  same  course.  This  method, 
too,  even  for  those  who  have  already  studied  per- 
spective— using  distance-points,  etc. — is  to  be  rec- 
ommended in  order,  that  the  subject  may  be  made 
perfectly  clear  to  them. 

The  perspective  of  interiors  (Problems  XVI- 
XVIII)  may  be  sometimes  be  advantageously  post- 
poned until  the  remaining  problems  have  been 
worked. 

FRANK  FORREST  FREDERICK. 
School  of  Industrial  Arts, 
Trenton,  New  Jersey. 
September  3,  1909. 


INTRODUCTION. 

THE  sense  of  color  and  the  sense  of  proportion  are  carefully  de- 
veloped by  art  teachers,  but  the  perspective  sense  is  largely  al- 
lowed to  take  care  of  itself. 

By  the  perspective  sense  is  meant  a  preception  of  the  relation  ex- 
isting between  straight  lines — their  apparent  convergence,  direction, 
length  and  position;  a  realization  of  what  is  meant  by  systems  of  lines 
(lines  that  have  the  same  direction)  ;  and  the  ability  to  think  of  sys- 
tems instead  of  individual  lines. 

The  lack  of  the  perspective  sense,  on  the  part  of  a  draftsman,  is 
as  apparent  in  his  work,  to  one  who  has  it,  as  the  lack  of  the  color  sense 
is  apparent  to  one  who  sees  and  appreciates  color. 

Students  are  prone,  in  drawing,  to  draw  a  line  here  and  another 
there — one  line  of  a  system,  then  a  line  of  another  system — trusting  to 
their  sense  of  proportion  alone  to  bring  the  drawing  out  correct  in  the 
end.  Asked  to  draw  the  interior  of  a  room,  or  a  street  scene,  the  stu- 
dent sees  only  a  maze  of  lines  because  his  ability  to  grasp  the  perspective 
of  the  viewr  as  a  whole  (his  perspective  sense)  has  not  been  developed. 

A  glance  at  the  illustrations  in  the  magazines  shows  how  lacking 
is  the  perspective  sense  even  among  many  of  the  professional  artists 
whose  ability  to  draw  the  figure  seems  almost  perfect.  We  see  figures 
standing  upon  a  floor  that  is  not  level,  or  upon  a  rug  one  edge  of 
which  only  rests  upon  the  floor,  or  dining  from  a  table  upon  which  a 
cup  could  hardly  be  made  to  stand.  These  illustrators,  in  their  school 
days,  probably  found  the  perspective  class  uninteresting,  as  do  most  art 
students.  , 

Is  this  the  fault  of  the  students,  or  does  the  fault  lie  in  the  manner 
in  which  the  subject  is  peresented?     , 

All  art  schools  offer  courses  in  mechanical  perspective,  and  in  many 
schools  that  make  a  specialty  of  educating  art  teachers  the  students  are 
required  to  take  the  course.  When  they  leave  school  they  either  forget 
all  about  the  theory  of  perspective,  or  regard  it  as  too  difficult  to  apply 
to  every-day  problems,  or  as  taking  too  much  time  to  be  taught  to  their 
own  pupils,  because  to  them  perspective  had  been  a  matter  of  tee-square 
and  triangle  only — its  application  to  practical  problems  and  freehand 


drawing  having  either  never  been  pointed  out,  or,  if  it  had,  so  obscured 
with  rules  and  methods  that  the  spirit  of  the  thing  was  entirely  missed. 
The  architect  and  the  designer  of  interior  decoration  must  be  mas- 
ters of  perspective:  it  is  a  part  of  their  stock  in  trade.  The  sculptor, 
the  painter  and  the  illustrator  have  equal  need  of  this  knowledge,  and 
every  one  who  draws  should  have  worked  perspective  mechanically 
long  enough  to  have  the  perspective  sense  so  developed  as  to  make  the 
application  of  the  rules  a  sort  of  second  nature,  even  if  the  theory  on 
\vhich  they  are  based  be  afterward  forgotten. 

Time  was  when  drawing  masters  believed  that  a  course  in  mech- 
anical perspective  should  be  followed  before  attempting  to  draw  objects 
freehand.  There  is  something  in  this  old  idea.  If  a  student  could 
draw  a  cube,  for  example,  in  mechanical  perspective — carrying  all  lines 
out  to  their  proper  vanishing  points — they  believed  (and  very  properly) 
that  his  freehand  drawing  of  the  same  cube  would  be  more  likely  to  be 
correct.  The  better  plan  is  to  carry  on  freehand  and  mechanical  per- 
spective together;  for  each  helps  the  other,  especially  if  the  student  is 
taught  to  apply  in  his  freehand  work  the  principles  illustrated  by  his 
course  in  mechanical  drawing. 

This  course  in  mechanical  perspective  is  planned  for  students  of  the 
high  school  age  who  have  already  received  some  training  in  mechanical 
drawing,  enough,  at  least,  to  understand  Plates  I  and  II. 

It  is  given  the  title  of  "Simplified  Mechanical  Perspective,"  as  the 
attempt  is  made  to  consider  the  essentials  that  will  develop  the  perspec- 
tive sense  and  enable  the  student  to  apply  his  knowledge  to  practical 
problems. 

It  is  thought  that  in  no  other  work  on  perspective  is  the  practical 
application  of  the  subject  to  interesting  and  every-day  problems  made 
so  direct. 


THE  PERSPECTIVE  DIAGRAM. 


THE   PERSPECTIVE  DIAGRAM. 

IN  Fig.  1,  Plate  1,  line  A-B  represents  a  horizontal  plane  upon 
which  a  spectator  is  standing.  The  distance  between  the  point 
marked  E.  (Eye)  and  the  point  marked  S.  P.  (Station  Point) 
represents  the  distance  the  spectator's  eye  is  above  the  horizontal  plane. 

The  spectator  is  supposed  to  be  looking  at  a  cube  the  plan  of  which 
(a-b-c-d)  is  seen  in  Fig.  2. 

An  imaginary  vertical  plane,  at  right  angles  to  the  direction  in 
which  the  spectator  is  looking,  is  placed  in  front  of  the  cube.  This  plane 
showrs  in  Fig.  1  as  a  vertical  line — the  edge  view  of  the  plane — and  in 
Fig.  2  as  a  line  upon  the  horizontal  plane — its  top  view,  or  plan,  called 
the  trace  of  the  vertical  plane  (Tr.  V.  PI.) 

Visual  rays  pass  from  the  eye  to  the  corners  of  the  cube  and  inter- 
sect the  vertical  plane  as  seen  in  Figs.  1  and  2.  If  these  points  of  in- 
tersection should  be  connected  by  lines  a  perspective  of  the  cube  would 
be  obtained  upan  the  vertical  plane. 

As  it  is  ^  not  practicable  to  draw  upon  this  vertical  plane,  a  nearer 
plane  called  the  picture  plane  (P.  PL)  is  placed  at  any  convenient  dis- 
tance from  the  spectator — as  the  picture  plane  in  Fig.  3,  shown  in  Fig. 
4  by  the  picture  line  (P.  L.) — the  line  of  intersection  of  the  picture 
plane  and  the  horizontal  plane. 

If  the  points  of  intersection  of  the  visual  rays  with  the  vertical 
plane  are  projected  to  the  picture  plane,  the  perspective  upon  the  pic- 
ture plane  will  be  the  same  as  the  perspective  upon  the  vertical  plane. 
Thus,  in  Fig.  4,  d-e  is  the  same  as  a-b  the  apparent  length  of  b-g,  and 
e-f  is  the  same  as  b-c  the  apparent  length  of  b-h. 

A  horizontal  plane  passing  through  the  spectator's  eye,  Fig.  1,  in- 
tersects the  vertical  plane  in  a  horizontal  line,  the  horizon,  not  seen  in 
Figs.  1,  2  and  3  as  it  is  upon  the  vertical  plane.  Its  position  may  be 
found,  however,  by  projecting,  by  line  1-2,  Fig.  3,  its  distance  above  the 
horizontal  plane  to  the  picture  plane,  and  then  revolving  it  (with  point 
R.  as  center)  to  coincide  with  the  horizontal  plane.  It  is  then  seen  as 
in  Fig.  4.  This  revolution  of  the  horizon  ( H )  from  its  position  upon  a 
vertical  plane  to  a  horizontal  plane  is  necessary  in  order  that  the  horizon 


SIMPLIFIED  MECHANICAL  PERSPECTIVE. 


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10 


THE  PERSPECTIVE  DIAGRAM. 

may  be  upon  the  same  plane  (as  a  sheet  of  paper)  as  the  picture  line, 
the  trace  of  the  vertical  plane,  and  the  station  point. 

The  point  directly  opposite  the  eye  on  the  vertical  plane  in  the 
horizon  is  called  the  center  of  vision,  seen  in  Fig.  2,  at  C.  V.  The  line 
connecting  the  S.  P.  with  the  C.  V.,  Fig.  2,  is  called  the  line  of  direc- 
tion (L.  of  D.) 

The  points  and  lines  so  far  found  constitute  the  perspective  dia- 
gram, Fig.  5,  Plate  II. 

TO    LAY   OUT    A    PERSPECTIVE    DIAGRAM. 

When  laying  out  a  perspective  diagram  upon  which  a  perspective 
is  to  be  drawn,  the  first  thing  to  determine  is  the  scale — a  quarter,  half, 
or  inch  to  the  foot,  depending  upon  the  size  of  the  object  to  be  drawn 
and  its  distance  from  the  spectator.  The  first  point  to  locate  is  S.  P. 
In  the  problems  to  follow  each  S.  P.  is  located  in  its  relation  to  the 
margin  line  of  a  plate  laid  out  as  in  Fig.  8.*  Thus  "S.  P.  22/0//  to 
right  and  2'0"  above"  means  22'0"  to  the  right  of  the  left  margin  line 
and  2'0"  above  the  lower  margin  line.  After  S.  P.  is  located,  draw  a 
line  to  represent  the  L.  of  D.,  Fig.  5,  and  set  off  on  it,  from  S.  P.,  the 
distance  C.  V.  is  from  S.  P.,  and  draw  through  C.  V.,  at  right  angles 
to  L.  of  D.,  the  Tr.  V.  PI.  P.  L.  is  placed  wherever  convenient — gen- 
erally at  or  ne#r  S.  P.  H.  is  placed  as  far  above  P.  L.  as  the  eye  is 
supposed  to  be  above  the  level  of  the  base  of  the  object  to  be  drawn,  or 
as  far  below  P.  L.  as  the  base  of  the  object  to  be  drawn  is  supposed  to 
be  above  the  level  of  the  eye. 

TO  FIND  VANISHING  POINTS. 

In  working  a  problem  first  place  the  plan  at  the  required  angle 
with  Tr.  V.  PL,  as  the  square  A-B-C-D  in  Fig.  6,  and  find  the  van- 
ishing points  of  the  retreating  or  vanishing  lines. 

To  find  the  vanishing  point  (V.  P.)  of  any  system  of  lines  (lines 
that  have  the  same  direction),  follow  the  direction  of  any  one  line  (or 
element)  of  the  system  till  its  point  of  intersection  with  the  vertical 
plane  is  found.  This  point  will  be  the  V.  P.  of  the  entire  system. 
The  vanishing  points  of  all  horizontal  systems  not  parallel  to  the  ver- 
tical plane  are  in  the  horizon. 

*A1I  plates  are  horizontal — the  14"  edge  at  the  top — unless  otherwise  in- 
dicated. The  2"  margin  at  the  left  allows  for  binding. 

11 


SIMPLIFIED  MECHANICAL  PERSPECTIVE. 


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12 


THE  PERSPECTIVE  DIAGRAM. 

To  find  the  V.  P.  of  A-D  and  B-C,  Fig.  6,  draw  a  line  from  S.  P. 
parallel  to  these  lines  (in  this  case  at  an  angle  of  45°  with  Tr.  V.  PI.) 
to  cut  the  Tr.  V.  PI.  Point  X  is  found  to  be  the  V.  P.  of  the  system 
of  which  A-D  and  B-C  are  two  elements,  and  point  Y  the  V.  P.  of  the 
system  of  which  A-B  and  D-C  are  two  elements.  These  points  (X  and 
Y)  are  projected  to  H.  at  V.  P.  R.  (vanishing  point  right)  and  V.  P. 
L.  (vanishing  point  left)  and  become  the  vanishing  points  to  be  used 
in  working  the  problem.  They  are  projected  to  H.  in  order  that  their 
distance  from  the  horizontal  plane  may  be  known. 

After  the  vanishing  points  are  found,  draw  the  visual  rays  from 
the  corners  of  the  plan,  centering  at  S.  P.,  but  drawn  only  to  Tr.  V. 
PI.,  in  order  to  obtain  the  apparent  length  of  lines  in  the  plan  as  ex- 
plained in  connection  with  Fig.  4,  Plate  I. 


PROBLEMS.* 
PROBLEM  I. 

This  problem  illustrates  the  method  of  drawing,  at  a  scale  of  y$" 
=1'0",  the  perspective  of  a  square  (6'0"x6'0")  that  is  on  the  hori- 
zontal plane,  with  sides  making  angles  of  45°  with  Tr.  V.  PL,  20'0" 
from  S.  P.  and  9'0"  below  the  eye. 

*NOTE  TO  TE'ACHERS: — Instructors  should  prepare  original  problems,  to  follow 
each  problem  here  given,  that  their  pupils  may  thoroughly  understand  all  prin- 
ciples and  methods.  Students  may  be  assigned  problems  to  work  on  the  black- 
board, as  problems  in  geometry  are  often  demostrated  before  the  class. 

The  writer  has  found  that  some  of  the  strongest  students  in  perspective 
seem,  at  first,  unable  to  comprehend  the  subject — working  the  problems  by  "rule 
of  thumb" — but  when  real  objects  or  rooms  were  to  be  drawn,  the  whole  theory 
has  seemed  to  dawn  upon  them,  in  some  cases  in  a  moment.  Therefore  the 
teacher  should  not  feel  discouraged  if  some  students  are  slow  to  grasp  the  subject. 

It  is  the  writer's  opinion  that  the  study  of  mechanical  and  freehand  perspec- 
tive should  be  carried  on  at  the  same  time.  Every  problem  in  this  course,  with 
the  exception  of  the  first  six,  should  be  followed  by  a  freehand  exercise.  For 
example:  After  working  Problem  VII  a  similar  prism  should  be  placed  before 
the  class  to  be  drawn  freehand.  After  Problem  XV  a  similar  table  should  be 
drawn  freehand. 

In  the  public  schools  students  will  have  drawn  boxes,  books,  tables,  chairs, 
etc.,  for  years  before  they  are  old  enough  to  attempt  this  or  any  course  in  mech- 
anical perspective.  They  should,  however,  combine  the  study  of  freehand  with 
mechanical  perspective  for  in  their  earlier  work  they  have  drawn  without  the 
sureness  and  accuracy  that  is  developed  by  the  study  of  mechanical  perspective. 

13 


SIMPLIFIED  MECHANICAL  PERSPECTIVE. 

The  statement  of  the  diagram  is:  Scale  }4"=1'0".  S.  P.  22 '0" 
to  the  right  and  2'0"  above.  C.  V.  20'0"  from  S.  P.,  P.  L.  5'0" 
from  S.  P.,  H.  9'0"  above  P.  L. 

After  the  diagram  is  complete,  draw  the  square  (A-B-C-D), 
find  V.  P.  R.  and  V.  P.  L.,  and  the  points  of  intersection  with  Tr.  V. 
PI.  of  the  visual  rays  from  S.  P.  to  its  corners  (points  F.  A.  E.) 


As  point  A  in  the  plan  is  against  Tr.  V.  PL,  point  G  of  the  per- 
spective will  be  against  P.  L.  Draw  G — V.  P.  R.  and  project  point  E  to 
point  H.  G-H  is  the  perspective  of  A-B.  Draw  G — V.  P.  L.  and 
project  point  F  to  point  J.  G-J  is  the  perspective  of  A-D.  Draw 
J — V.  P.  R.  and  H — V.  P.  L.,  and  their  point  of  intersection,  I,  is  the 
perspective  point  of  C.  G-H-I-J  is  the  perspective  of  A-B-C-D. 

The  plan  may  be  placed  at  any  angle  with  Tr.  V.  PI.,  and  its 
vanishing  points  found  as  illustrated  above.  In  Fig.  7,  Plate  II,  a 
square  is  so  placed  that  two  sides  make  angles  of  30°  and  two  60°. 
In  Problem  II  the  V.  P.  R.  of  lines  at  60°  and  the  V.  P.  L.  of  lines 
at  30°  must  be  found  as  illustrated  in  Fig.  7. 


14 


THE  PERSPECTIVE  DIAGRAM. 


PROBLEM  II. 

Scale  #"=1'0".  S.  P.  3  TO"  to  the  right  and  2'0"  above.  C. 
V.  14'0"  from  S.  P.,  P.  L.  3'0"  from  S.  P.,  H.  6'0"  above  P.  L. 

In  this  problem  a  10'0"xl0'0"  square  is  so  placed  that  the  right 
side  makes  an  angle  of  60°  with  Tr.  V.  PL,  and  the  left  side  an  angle 
of  30°.  The  perspective,  though  correct,  appears  distorted  because  the 


VF7v-60 


spectator  (S.  P.)  was  placed  too  near  so  large  a  square.  Distortion  of 
the  perspective  will  also  result  if  the  plan  is  placed  too  far  to  the  right 
or  left  of  C.  V.  It  may,  however,  be  placed  a  short  distance  to  the 
right  or  left  of  C.  V.  without  serious  distortion  as  shown  in  Problem  III. 

PROBLEM  III. 

Scale  }4"=1'0".  S.  P.  22'0"  to  right  and  1'6"  above.  C.  V. 
2C'0"  from  S.  P.,  P.  L.  6'0"  from  S.  P.,  H.  6'0"  above  P.  L. 

In  this  problem  a  7'0"x7'0"  square,  with  sides  making  angles  of 
45°  with  Tr.  V.  PI.,  is  so  placed  that  its  nearest  corner  is  6'0"  to  the 
left  of  C.  V. 


IS 


SIMPLIFIED  MECHANICAL  PERSPECTIVE. 


Ill 


16 


THE  PERSPECTIVE  DIAGRAM. 

PROBLEM  IV. 

Scale  #"=1'0".  S.  P.  22'0"  to  right  and  I'O"  above.  C.  V. 
12'0"  from  S.  P.,  P.  L.  at  S.  P.,  H.  6'0"  above  P.  L. 

This  problem  illustrates  the  method  of  putting  into  perspective 
a  plan  that  is  beyond  the  vertical  plane.  The  square  is  9'0"x9'0", 
and  is  placed  5'0"  to  the  right  of  C.  V.  and  3'0"  beyond  Tr.  V.  PL 
Continue  side  B-A  to  cut  Tr.  V.  PI.  at  E.  Project  E  to  P.  L.  at  F. 
Draw  F — V.  P.  L.,  and  find  the  perspective  of  B-A  in  line  F — V.  P.  L. 
Having  located  in  perspective  one  side  of  the  square,  the  three  remain- 
ing sides  can  be  found  as  in  the  foregoing  problems.  If  corner  A  had 
been  in  line  with  the  L.  of  D.  the  intersection  of  line  F — V.  P.  L. 
with  L.  of  D.  would  have  been  the  perspective  of  corner  A. 


PROBLEM  V. 

Scale  J4"=1'0".  S.  P.  12'0"  to  right  and  2'0"  above.  C.  V. 
17'0"  from  S.  P.,  P.  L.  5'0"  from  S.  P.,  H.  6'0"  above  P.  L. 

Any  point  on  the  horizontal  plane  may  be  put  into  perspective  (as 
point  A  placed  at  random)  by  considering  the  point  as  the  end  of  a 
line  drawn  to  cut  Tr.  V.  PI.  at  any  convenient  angle — in  this  case  an 


17 


SIMPLIFIED  MECHANICAL  PERSPECTIVE. 


V.'P.L 


30: 


V.P.K. 


Z2E 


18 


SIMPLIFIED  MECHANICAL  PERSPECTIVE. 

angle  of  60°  to  the  left.     Putting  the  line  into  perspective  we  find,  of 
course,  the  perspective  of  its  end — as  point  A. 

After  finding  the  perspective  of  point  A  as  described  above,  find 
it  by  considering  the  same  point  as  the  end  of  a  line  making  an  angle 
of  30°  to  the  right. 

PROBLEM  VI. 

Scale  J4=1'0".  S.  P.  22'0"  to  right  and  2'0"  above.  C.  V. 
16'0"  from  S.  P.,  P.  L.  lO'O"  from  S.  P.,  H.  8'0"  below  P.  L. 

In  this  problem  a  square  9/0//x9/0//,  is  above  the  level  of  the  eye 
and  therefore  H.  is  placed  as  far  below  P.  L.  as  the  square  is  sup- 
posed to  be  above  the  level  of  the  eye. 

When  problems  are  lined-in  with  ink,  the  lines  drawn  at  the  given 
angles  from  S.  P.,  the  line  of  direction,  and  horizon  line  may  be  omitted 
to  avoid  confusion,  as  only  the  points  obtained  by  these  lines  are  nec- 
essary for  the  working  of  the  problems.  (See  Problems  VII-XII.) 

PROBLEM  VII. 

Scale  %"=1'0".  S.  P.  23'0"  to  right  and  2'0"  above.  C.  V. 
17'0"  from  S.  P.,  P.  L.  at  S.  P.,  H.  9'0"  above  P.  L.  In  this  problem 
a  rectangular  solid  6'0"x5'0"xl0'0"  rests  on  one  6'0"xl0'0"  face,  with 
sides  vanishing  to  right  and  left  at  45°.  The  plan  is  placed  as  in  the 
foregoing  problems.  One  elevation,  all  that  is  needed  to  secure  the 
heighth  of  the  solid,  is  placed  upon  P.  L.  at  one  side  of  the  problem. 

The  nearest  vertical  edge  of  the  solid  rests  against  the  vertical 
plane  and  therefore  its  perspective  will  be  upon  the  picture  plane.  The 
true  length  of  this  edge  (5'0")  may  be  set  off  at  A-B,  or  projected 
from  the  elevation  by  line  C-A. 

In  this  system  of  perspective  all  heights  are  secured  from  eleva- 
tions; and  all  heights  (as  in  any  system  of  perspective)  must  be  meas- 
ured or  located  upon  the  picture  plane,  for  there  only  do  they  appear 
of  their  true  length. 

PROBLEM  VIII. 

Scale  y4"=\'Q".  S.  P.  22'0"  to  right  and  2'0"  above.  C.  V. 
17'0"  from  S.  P.,  P.  L.  at  S.  P.,  H.  9'0"  above  P.  L. 

In  this  problem  a  square  prism,  base  8'0"x8'0",  altitude  14'0", 

19  * 


SIMPLIFIED  MECHANICAL  PERSPECTIVE. 


T7TTT 


D 


M 


20 


THE  PERSPECTIVE  DIAGRAM. 

with  sides  vanishing  to  right  and  left  at  45°  is  drawn.  The  lower  base 
is  upon  the  horizontal  plane,  the  upper  is  above  the  level  of  the  eye. 
Its  height  is  found  as  in  Problem  VII. 

PROBLEM  IX. 

Scale  #"=1'0".  S.  P.  22'0"  to  right  and  3'0"  above.  C.  V. 
15'0"  from  S.  P.,  P.  L.  at  S.  P.,  H.  5'0"  above  P.  L.  In  this  prob- 
lem a  square,  12'0"xl2'0",  one  of  whose  sides  (A-B)  rests  against  Tr. 
V.  PL,  is  drawn.  Sides  A-D  and  B-C  make  with  Tr.  V.  PL  angles  of 
90°.  To  find  their  V.  P.  draw  from  the  S.  P.  a  line  parallel  to  them  to 


cut  Tr.  V.  PL  This  V.  P.  is  found  to  coincide  with  C.  V.  Projecting 
this  V.  P.  to  H.  (as  other  vanishing  points  are  projected)  the  point 
marked  new  C.  V.  is  found.  This  point  is  the  V.  P.  of  the  system  of 
which  lines  A-D  and  B-C  are  two  elements. 

The  perspective  of  the  square  in  this  problem  can  be  drawn  in  the 
usual  manner,  or  by  the  use  of  diagonals.  As  diagonal  A-C  makes  an 
angle  to  the  right  of  45°,  it  will,  if  put  into  perspective,  cut  line  H- 
New  C.  V.  at  F  and  make  H-F  equal  to  H-G.,  and  diagonal  B-D,  if 
put  into  perspective,  will  locate  D  in  perspective  at  E. 


21 


SIMPLIFIED  MECHANICAL  PERSPECTIVE. 


3H. 


Y 


Elevated  PL 
?         P,L 


22 


THE  PERSPECTIVE  DIAGRAM. 

In  Problems  I,  III,  IV,  and  VI  one  diagonal  of  the  perspective 
will  be  a  horizontal  line  and  the  other  will  vanish  at  the  New  C.  V. 
The  perspective  of  the  center  of  any  rectangle  in  perspective  may  be 
found  by  drawing  its  diagonals 


PROBLEM  X. 

Scale  y2"=l'Q".  S.  P.  ll'O"  to  right  and  I'O"  above.  C.  V. 
8'0"  from  S.  P.,  P.  L.  at  S.  P.,  H.  4'0"  above  P.  L.  In  this  problem 
a  square,  4'0"x4'0",  with  two  sides  parallel  to  Tr.  V.  PI.,  is  2'0"  be- 
yond the  vertical  plane.  Its  perspective  is  obtained  by  applying  the 
method  of  finding  points  beyond  the  vertical  plane  illustrated  in  Prob- 
lems IV  and  V. 

PROBLEM  XL 

Scale  J4"=1'0".  S.  P.  22'0"  to  right  and  2'0"  above.  C.  V. 
16'0"  from  S.  P.,  P.  L.  at  S.  P.,  H.  12'0"  above  P.  L.  In  this  prob- 
lem an  equilateral  triangular  prism  rests  on  one  8'0"xll'0"  face  as 
shown  by  the  plan.  The  altitude  of  the  triangular  base  is  put  into  per- 
spective by  projecting  it  to  A-B,  drawing  A — V.  P.  L.,  and  projecting 
point  C  to  cut  A — V.  P.  L. 

The  visible  triangular  base  of  the  prism  is  included  in  a  ver- 
tical plane  vanishing  to  the  left.  Therefore  any  vertical  distance  in 
this  plane  must  be  first  set  off  on  the  intersection  of  this  vertical  plane 
with  the  picture  plane  (as  A-B)  and  then  carried  into  perspective. 


PROBLEM  XII. 

Scale  ^"=1'0".  S.  P.  ll'O"  to  right  and  I'O"  above.  C.  V. 
8'0"  from  S.  P.,  P.  L.  at  S.  P.,  H.  6'0"  above  P.  L.  In  this  problem 
a  square  plinth  5'6"x5'6",  altitude  3'0",  with  sides  at  45°,  is  2'0" 
above  the  horizontal  plane.  As  the  lower  base  is  2'0"  above  the  hori- 
zontal plane,  an  elevated  picture  line,  (El.  P.  L.)  2'0"  above  P.  L. 
may  be  used.  Whenever  a  horizontal  surface,  that  is  not  the  upper 
base  of  an  object  on  the  horizontal  plane,  is  to  be  put  into  perspective 
it  is  well  to  use  an  El.  P.  L. 


23 


SIMPLIFIED   MECHANICAL  PERSPECTIVE. 


THE  PERSPECTIVE  OF  FURNITURE  AND  INTERIORS. 

IT  MAY  have  occurred  to  those  who  are  working  these  problems, 
that  the  Tr.  V.  PI.  might  be  used  as  H.,  the  points,  found  by 
drawing  lines  at  the  required  angles  from  S.  P.,  as  the  vanishing 
points  for  the  problems,  and  that  the  P.  L.  might  be  placed  as  far  below 
Tr.  V.  PI.  as  the  eye  is  supposed  to  be  above  the  horizontal  plane. 
This  is  true,  and  Problems  I  to  VI  might  have  been  so  worked,  but  in 
this  system  of  perspective — known  as  the  "Plan  Method" — where  the 
plan  of  the  object  to  be  put  into  perspective  is  drawn,  this  plan  and  the 
working  lines  of  the  problem  would  be  confused  with  the  perspective  if 
the  picture  plane,  with  H.,  was  not  moved  nearer  the  spectator. 

Students  who  have  followed  these  problems  should  now  be  suffi- 
ciently familiar  with  the  subject  to  be  on  the  lookout  for  "short  cuts" 
in  locating  points  and  lines  by  means  of  diagonals,  etc,  and  should  learn 
to  distinguish  between  lines  necessary  for  the  complete  solving  of  the 
problems  and  lines  used  only  to  obtain  some  required  point.  It  should 
no  longer  be  necessary  to  carry  all  lines  out  to  their  vanishing  points 
in  order  to  appreciate  their  direction,  and  lines  of  projection  from  Tr. 
V.  PI.  to  the  perspective  should  be  omitted  if  likely  to  confuse  the  prob- 
lem. If  the  proper  degree  of  hardness  of  pencil  for  the  paper  used  is 
found,  all  working  lines  may  be  made  of  a  delicate  lightness  that  will 
permit  all  to  be  seen  without  causing  confusion. 

Success  in  working  the  following  problems  will  depend  largely  upon 
a  sharply  pointed  hard  pencil. 

PROBLEM  XIII. 

Scale  y2"—\'Q".  S.  P.  ll'O"  to  right  and  I'O"  above.  C.  V. 
9'0"  from  S.  P.,  P.  L.  at  S.  P.,  H.  6'0"  above  P.  L.  In  this  prob- 
lem a  box  3'0"x5'0"  and  2'0"  deep,  with  cover  open  at  angle  of  60°,  is 
placed  at  an  angle  of  45°  with  Tr.  V.  PI.  The  box  is  put  into  perspec- 
tive as  is  the  prism  in  Problem  VII. 

The  edge  of  the  cover  is  seen  as  line  A-B  in  the  plan.  Drawing 
a  vertical  line  from  C  we  have  a  vertical  in  which  the  perspective  of  A 
will  be  found.  Project  point  D  to  E  and  draw  E — V.  P.  L.  Where 
E — V.  P.  L.  cuts  the  vertical  the  perspective  of  A  is  found. 

24 


THE  PERSPECTIVE  OF  FURNITURE. 

The  same  vertical  plane  includes  the  end  of  the  box  and  the  edge 
of  the  cover  as  it  opens.  Any  vertical  distance  in  this  plane  must  be 
first  set  off  on  its  intersection  with  the  picture  plane  (as  E — S.  P.)  and 
then  carried  into  perspective. 

This  problem  will  have  but  a  small  part  of  its  possible  value  to 
students  if  it  is  not  followed  by  a  practical  problem.  Bring  a  trunk  into 
the  drawing  room,  raise  the  cover  to  some  known  angle,  and  place  the 
student  who  is  to  draw  the  perspective  a  certain  number  of  feet,  as 


wr. 


8'0",  from  the  nearest  corner  of  the  trunk.  The  point  on  the  floor 
under  the  student's  eye  becomes  the  S.  P.  The  distance  upon  the  floor 
from  S.  P.  to  the  nearest  corner  of  the  trunk  (C.  V.)  becomes  the  L. 
of  D.  The  distance  the  eye  is  from  the  floor  gives  the  distance  H. 
must  be  placed  above  P.  L.  Measuring  the  trunk  to  get  its  dimensions, 
and  turning  it  so  that  it  makes  some  known  angle  with  the  assumed 
vertical  plane,  and  adopting  a  scale  for  the  drawing,  a  perspective  should 
be  drawn.  S.  P.,  L.  of  D.,  Tr.  V.  PL,  P.  L.  and  H.  may  be  drawn 
upon  the  floor  with  chalk. 

If  two  students  work  together,  and  with  tape  line  find  the  dis- 
tances and  measurements,  problems  of  this  character  become  more  inter- 
esting. 

25 


SIMPLIFIED  MECHANICAL   PERSPECTIVE. 


TTV  , 


26 


THE  PERSPECTIVE  OF  FURNITURE. 

PROBLEM  XIV. 

Scale  1"=1'0".  S.  P.  2'9"  to  right  and  6"  above.  C.  V.  4'6" 
fiom  S.  P.,  P.  L.  at  S  P.,  H.  3'0"  above  P.  L.  In  this  problem  a 
set  of  steps,  rise  6",  tread  9"  and  2'0"  long,  make  an  angle  of  30° 
to  the  right.  In  the  perspective  the  width  of  the  treads  is  obtained  from 
the  plan  and  the  height  of  the  risers  from  the  elevation,  being  first  set 
off  on  the  L.  of  D.,  and  then  carried  into  perspective  by  lines  vanishing 
at  V.  P.  R. 

Two  or  three  of  the  lower  steps  of  any  stairway  provides  a  prac- 
tical exercise  to  apply  this  problem. 

PROBLENf  XV. 

In  this  problem  a  table  (measurements  given  on  the  plan  and  ele- 
vation) is  drawn  as  it  would  appear  to  a  spectator  whose  eye  is  3'6" 
from  the  floor,  and  who  is  so  placed  that  the  point  on  the  floor  (S  P.) 
directly  under  his  eye  is  4'0"  from  the  point  on  the  floor  directly  under 
the  nearest  corner  of  the  top  of  the  table. 

The  statement  of  the  diagram  is  as  follows : 

Scale  1"=1'0".  S.  P.  5'6"  to  right  and  3"  above.  C.  V.  4'0" 
from  S.  P.,  P.  L.  at  S.  P.,  H.  3'6"  above  P.  L. 

The  table  top  is  one  inch  thick  and  2'11"  from  the  floor.  First 
put  the  top  in  perspective  by  using  an  El.  P.  L.,  2'11"  from  P.  L.,  and 
then  the  legs,  using  P.  L.  In  the  location  of  the  nearest  corner  of  the 
nearest  leg  on  the  floor  apply  Problem  IV.1 

It  is  but  a  step  from  drawing  objects  in  a  room  to  the  room  itself. 
The  same  principles  apply  and  the  method  is  the  same. 

Plate  III  (not  to  be  worked  by  students)  reproduces  a  perspective 
drawing  of  an  inglenook  the  plan  of  which  is  shown  by  Fig.  9.  The 
drawing  is  introduced  at  this  point  in  the  course  to  illustrate  the  method 
of  approaching  a  problem  of  this  character. 

'NOTE  TO  TEACHERS. — When  selecting  furniture  for  students  to  measure  and 
draw  in  perspective,  care  should  be  taken  to  select  very  simple  examples,  as, 
possibly,  the  book-rack  or  shelves  made  by  the  students  in  the  wood  shop.  (See 
accompanying  illustrations.)  If  small  these  may  be  placed  upon  a  table  which 
becomes  the  horizontal  plane  for  the  problem. 

After  students  have  become  familiar  with  perspective  and  accustomed  to 
working  problems — in  other  words,  when  their  perspective  sense  has  become 
developed — they  should  be  assigned  more  complicated  and  difficult  problems,  the 
important  lines  of  which  should  be  found  mechanically  and  the  details  added 
freehand. 

27 


SIMPLIFIED  MECHANICAL  PERSPECTIVE. 


By  measuring  it  \vas  found  that  a  point  on  the  floor  directly  under 
the  spectator's  eye  (S.  P.)  was  12'0"  from  the  point  marked  Y  in  the 
plan,  Fig.  9.  His  eye  was  found  to  be  3'8"  above  the  floor. 

The  first  step  taken  in  drawing  the  per- 
spective of  this  inglenook,  was  the  drawing  of 
the  plan.  The  next  step  was  the  location,  at  the 
same  scale,  of  S.  P.,  L.  of  D.,  Tr.  V.  PL,  P.  L., 
and  H.  in  the  order  named.  As  the  eye  chanced 
to  be  directly  in  line  with  the  left  wall  (Y-Z), 
Y-Z  in  the  plan  was  continued  12'0"  and  the  S. 
P.  for  the  problem  was  found.  S.  P. — X  (the 
L.  of  D.)  was  next  drawn,  and  Tr.  V.  PL  was 
drawn  at  right  angles  to  the  L.  of  D.  through 
point  Y.  The  paper  was  then  taken  from  the 
board  and  repinned  with  Tr.  V.  PL  as  a  hori- 
zontal line.  P.  L.  was  placed  at  S.  P.  and  H. 
placed  3'8"  above  P.  L.  V.  P.  L.  was  located 

by  projecting  point  Y  to  H.,  and  V.  P.  R.  by  drawing  from  S.  P.,  par- 
allel to  Y-W,  to  cut  Tr.  V.  PL,  and  then  projecting  the  point  found 


3/P 


Fto-.S>. 


28 


THE  PERSPECTIVE  OF  FURNITURE. 


PLATLffl 


29 


SIMPLIFIED  MECHANICAL  PERSPECTIVE. 

to  H.  V7.  P.  R.  falls  outside  the  margin  line.  When  drawing  per- 
spectives of  interiors,  students  should  use  large  drawing  boards,  or 
fasten  small  boards  to  the  top  of  tables,  to  secure  room  for  the  vanish- 
ing points.  These  points,  when  located,  can  be  kept  by  driving  pins 
into  the  boards  or  table.  The  elevation  was  then  drawn  with  P.  L.  as 
base  line. 

The  important  lines  in  the  perspective  of  the  inglenook  were  ob- 
tained from  the  plan  and  elevation,  but  the  details  were  drawn  by  guess. 
If  the  perspective  had  been  drawn  at  a  larger  scale  (1"=1'0"  was  used) 
these  could  have  been  drawn  accurately.  Architects  and  designers  for 
interior  decoration  often,  for  convenience,  draw  perspectives  at  small 
scale  and  then  enlarge  them  to  any  size  desired. 

If  the  lines  to  obtain  widths  become  confusing  on  account  of  their 
number,  they  can  be  drawn  in  sets  and  each  set  erased  before  the  next 


Tr.V.Pf 


30 


Fig'.ll. 


is  drawn.     In  Plate  III  the  set  used  to  obtain  the  seat  was  erased  before 
the  set  used  to  obtain  the  fire-place  were  drawn. 

In  working  perspective  problems  much  experiment  is  often  nec- 
essary to  get  the  perspective  upon  the  paper  where  wanted.  If  the  plan 
and  elevation  be  drawn  and  then  cut  apart  and  pasted  or  pinned  upon  the 
paper  upon  which  the  perspective  is  to  be  drawn,  much  time  may  be 
saved  as  their  position  may  be  changed  without  going  to  the  trouble  of 
re-drawing. 

PROBLEM  XVI. 

In  this  problem,  Fig.  10,  a  spectator,  whose  eye  is  4'0"  from  the 
floor,  is  supposed  to  be  standing  in  a  door  at  the  end  of  a  room  19'0"x 


30 


THE  PERSPECTIVE  OF  FURNITURE. 


XVI 


XV  I  L 


26'0".  He  assumes  the  vertical  plane  to  be  18'0"  from  his  eye.  The 
perspective  represents  that  part  of  the  room  (8'0")  lying  beyond  the 
vertical  plane.  The  statement  of  the  diagram  will  be:  Scale  %"=1'0". 
S.  P.  22'0"  to  right  and  3'0"  above  .  C.  V.  18'0"  from  S.  P.,  P.  L. 
at  S.  P.,  H.  4'0"  above  P.  L. 

31 


SIMPLIFIED  MECHANICAL  PERSPECTIVE. 

Put  the  room  into  perspective  according  to  Problem  IX,  and  draw 
the  door  and  windows  3'0"  wide.  The  height  of  the  room,  the  door 
and  windows  is  shown  by  a  section  of  the  wall  of  the  room. 


XVIII. 


VPL  -; 


H    YPR 


PL 


PROBLEM  XVII. 

In  this  problem,  Fig.  11,  a  spectator  whose  eye  is  4'0"  above  the 
floor,  is  standing  15'0"  from  the  corner  of  the  room.  The  Tr.  V.  PI. 
is  assumed  to  be  lO'O"  distant.  The  drawing  represents  the  perspective 
of  that  part  of  the  room  (5'0")  lying  beyond  the  vertical  plane.  The 
diagram  is  drawn  as  follows: 


32 


THE  PERSPECTIVE  OF  FURNITURE. 


Scale  J£"=1'0".  S.  P.  ll'O"  to  right  and  6"  above.  C.  V.  lO'O" 
from  S.  P.,  P.  L.  I'O"  from  S.  P.,  H.  4'6"  above  P.  L.  The  door  is 
3'0"  wide  and  the  floor  is  divided  in  2'0"  squares. 

When  drawing  interiors,  where  the  distance  from  S.  P.  to  C.  V. 
is  less  than  the  height  of  the  room,  P.  L.  may  be  placed  wherever  con- 
venient— above  the  plan  or  below  S.  P.,  Fig.  12.  If  H.  is  kept  the 
required  distance  from  P.  L.,  and  the  widths  are  obtained  from  Tr.  V. 
PI,  the  perspective  will  be  the  same  as  if  drawn  upon  a  P.  L.  placed  at 
or  near  S.  P.  (See  Problem  XVIII.) 

PROBLEM  XVIII. 

(For  this  problem  the  8"  side  of  the  margin  line  is  considered  as 
the  top.) 

Scale  ^"=1'0".  S.  P.  8'0"  to  right  and  4'9"  above.  C.  V. 
9'0"  from  S.  P.,  P.  L.  2'0"  above  lower  margin  line,  H.  4'0"  above 
P.  L.  The  spectator,  whose  eye 

is  4'0"  from  the  floor,  is  sup- 
posed to  be  standing  16'0'' 
from  the  corner  of  a  room.  The 
vertical  plane  is  placed  9'0" 
from  his  eye.  The  ceiling  of 
the  room  is  lO'O"  from  the  floor 
and  therefore  P.  L.  is  placed 
below  S.  P.  The  doorway  is 
7'6"  high,  the  fire-place  open- 
ing is  2/0"  high,  the  tiles  are  6" 
square  and  the  picture  mould- 
ing l/6//  from  the  ceiling.  A 
rug  3'0"  square  is  placed  in  the 
center  of  the  door  and  extends 
through  into  the  adjoining  room 
The  shelf  projects  4"  from  the 
chimney  breast  and  is  on  the 
level  of  the  eye.  Point  A  is 
located  as  point  A  in  Problem 
V.  Part  of  the  hearth  is  found 
^  '  '  to  Pr°Ject  m  front  of  the  verti- 

cal plane.     This  frequently  happens  when  designing  interiors,  and  if  the 
projection  is  not  too  great  the  drawing  is  not  seriously  distorted.     To 


P.L. 


33 


SIMPLIFIED  MECHANICAL  PERSPECTIVE. 

find  the  perspective  of  lines  extending  in  front  of  the  vertical  plane,  find 
the  perspective  of  the  ends  of  the  lines  that  are  beyond  the  vertical  plane, 
and  continue  the  lines  until  they  meet  in  front  of  the  picture  plane. 

After  students  have  worked  Problems  XVI,  XVII  and  XVIII, 
they  should  be  assigned  ends  and  corners  of  rooms  and  halls  to  be  drawn 
in  perspective  as  practical  problems  to  apply  the  knowledge  gained. 
Before  students  undertake  the  remaining  problems  in  this  series  they 
should  be  able  to  draw  in  perspective  any  view  of  any  room  from 
any  point. 


The  practice  and  experience  gained  in  this  work  is  not  limited  to 
the  actual  drawing  of  the  perspective.  To  measure  a  room  and  draw 
its  plan  and  elevation  or  section — to  decide  upon  the  angle  the  sides  of 
the  room  shall  make  with  the  vertical  plane — to  locate  to  the  best  ad- 
vantage, the  station  point  and  the  vertical  plane,  gives  an  all-round 
training  in  mechanical  drawing  that  is  quite  as  valuable  to  the  student 
as  the  development  of  his  perspective  sense. 

PROBLEM  XIX. 

A  student  whose  perspective  sense  has  not  been  developed  always 
has  trouble  when  drawing  the  gables  and  eaves  of  houses,  and  the  lines 
of  intersection  of  chimneys  with  roofs.  Some  of  our  best  landscape 


34 


THE  PERSPECTIVE  OF  FURNITURE. 

painters  seem  unable  to  handle  this  really  simple  problem  in  perspective. 

Scale  #"=1'0".  S.  P.  22'0"  to  right  and  I'O"  above.  C.  V* 
12'0"  from  S.  P.,  P.  L.  at  S.  P.,  H.  lO'O"  above  P.  L. 

After  drawing  the  roof,  draw  the  top  of  the  chimney  from  an  ele- 
vated picture  line  as  far  (5'0")  above  P.  L.  as  the  top  of  the  chimney 
is  above  the  horizontal  plane. 

To  find  the  line  of  intersection  of  the  chimney  with  the  roof,  con- 
sider the  right  side  of  the  chimney  as  included  in  a  vertical  plane  cutting 
the  roof.  The  line  of  intersection  of  this  vertical  plane  with  thereof 
is  found  as  follows: 

Continue  the  side  of  the  chimney  to  point  A.  Project  A  to  B. 
Draw  B — V.  P.  R.  to  find  C.  Draw  C-D,  a  vertical  line,  and  connect 


I2'o" 


D  with  V.  P.  R.  Project  the  width  of  the  right  side  of  the  chimney  to 
D — V.  P.  R.  and  the  intersection  of  the  right  side  of  the  chimney  with 
the  roof  is  found. 

The  line  of  intersection  of  the  left  side  with  the  roof  is  found  by 
projecting  the  point  of  intersection  of  the  ridge  of  the  roof  with  the 
chimney  to  its  perspective  and  E-F  is  found — a  short  line  but  quite  as 
important  as  any  line  in  the  problem. 


35 


THE  PERSPECTIVE  OF  FURNITURE. 

PROBLEM  XX. 

Scale  *4"=1'0".  S.  P.  22'0"  to  right  and  2'0"  above.  C.  V. 
14'0"  from  S.  P.,  P.  L.  at  S.  P.,  H.  7'0"  from  P.  L. 

Draw,  first,  the  rectangular  prism  representing  the  body  of  the 
house  and  the  triangular  prism  representing  the  roof.  Then  draw, 
from  an  elevated  picture  line,  the  triangular  prism,  which,  with  the 
bases  omitted,  becomes  the  projecting  eaves  and  gables. 


36 


(.J 


THE  PERSPECTIVE  OF  CIRCLES. 


THE  PERSPECTIVE  OF  CIRCLES. 

A  CIRCLE  may  appear  as  a  circle,  a  line  or  as  an  ellipse.   It  appears 
of  its  true  shape  when  it  is  at  right  angles  to  the  direction  in 
which  the  spectator  is  looking,  as  a  line  when  included  in  a  plane 
that  passes  through  the  eye,  and  as  an  ellipse  when  the  circle  is  in  any 
other  position  in  relation  to  the  eye. 

_  If    a    circle    is    inscribed 

within  a  square  there  are 
four  points,  1,  3,  5  and  7, 
Fig.  13,  where  the  circum- 
ference of  the  circle  is  tan- 
gent to  the  sides  of  the  square, 
and  four  points,  2,  4,  6  and 
8,  where  the  circumference 
of  the  circle  intersects  the  di- 
agonals of  the  square. 

When  a  circle  is  put  into 
perspective  it  is  usual  to  draw 
a  square  about  it,  find  the 
eight  points  just  mentioned, 
put  the  square  into  perspec- 
and  draw  the 


(the  perspective  of  the  circle)   through  the  perspective  of  these  points. 

PROBLEM  XXI.1 

Plate  vertical.  Scale  1"=!'  0"  S.  P.  4'  0"  to  right  and  3"  above. 
C.  V.  3'  9"  from  S.  P.,  P.  L.  at  S.  P.,  H.  2'  0"  above  P.  L. 

In  this  problem  a  circle,  6'  0"  in  diameter,  is  directly  in  front  of  the 
spectator.  A  square,  with  sides  tangent  to  the  circumference,  is  drawn 
and  points  1,  3,  5  and  7  found.  By  drawing  the  diagonals  of  the  square 
points  2,  4,  6  and  8  are  found.  Putting  the  square  into  perspective 

'NOTE  TO  TEACHERS: — When  students  begin  the  study  of  the  circle  in  per- 
spective it  is  well  to  draw  circles  upon  the  floor,  or  upon  the  blackboard,  as 
problems  to  be  worked  by  the  class.  These  should  be  drawn  large  (six  or  eight 
feet  in  diameter)  and  the  students  placed  near  them,  otherwise  their  drawings 
will  be  too  small  to  be  worked  accurately. 


37 


SIMPLIFIED  MECHANICAL  PERSPECTIVE. 


t 


\ 


t 


4- -4- 


38 


THE  PERSPECTIVE  OF  CIRCLES. 

according  to  the  method  explained  in  Problem  IX,  the  perspective  of 
the  circle — the  ellipse — may  be  drawn  through  the  perspective  of  the 
eight  points  1  to  8  inclusive. 

PROBLEM  XXII. 

Plate  vertical.     Scale  X"=1'0".     S.  P.  16'0"  to  right  and  I'O" 
above.   C.  V.  15'  0"  from  S.  P.,  P.  L.  at  S.  P.,  H.  12' 0"  above  P.  L. 
A  square,  19'  0"  x  19'0"  on  the  horizontal  plane,  has  its  sides  van- 
ishing to  right  and  left  at  45°.     Within  the  square  is  a  circle  19'0"  in 
diameter. 


To  find  the  perspective  of  the  circle  draw  the  perspective  of  the 
square  with  its  diagonals  and  diameters,  and  find  the  perspective  of  the 
points  1  to  8.  2,  4,  6  and  8  are  found  at  the  ends  of  the  diameters,  1 
and  5  on  the  diagonal  parallel  to  the  picture  plane,  as  points  are  usu- 
ally located,  and  points  3  and  7,  on  the  diagonal  at  right  angles  to  the 
picture  plane,  according  to  problems  IV  and  V. 

PROBLEM  XXIII. 

Plate  horizontal.    Scale  Y4=V  0".    S.  P.  22'  0"  to  right  and  V  0" 
above.     C.  V.  20'  0"  from  S.  P.,  P.  L.  at  S.  P.,  H.  8'  0"  above  P.  L. 
A  vertical  circle,  14'  0"  in  diameter,  vanishes  to  the  right  at  45°. 


39 


SIMPLIFIED  MECHANICAL  PERSPECTIVE. 

PROBLEM  XXIV. 

Plate  vertical.  Scale  #"=!'  0".  S.  P.  16'  0"  to  right  and  7'  0" 
above.  C.  V.  15' 0"  from  S.  P.,  P.  L.  2' 0"  from  lower  margin  line, 
H.  19'  0"  above  P.  L. 

In  this  problem  a  circular  plinth,  base  16'  0"  in  diameter,  altitude 
ll'O",  rests  on  its  side  in  the  horizontal  plane  which  is  19'0"  below 


the  level  of  the  eye.  The  axis  of  the  plinth  vanishes  to  the  right  at  45°. 
A  lowered  picture  line  is  used,  to  prevent  confusion  of  lines,  because 
the  distance  from  S.  P.  to  C.  V.  is  less  than  the  diameter  of  the  base 
of  the  plinth,  and  also  because  the  distance  from  P.  L.  to  H.  is  greater 
than  the  distance  from  S.  P.  to  C.  V.  P.  L.  can  be  placed  wherever 
convenient  providing  it  is  at  a  greater  distance  from  Tr.  V.  PI.  than  H. 
is  from  P.  L. 


40 


THE  PERSPECTIVE  OF  CIRCLES. 


Put  the  visible  base  into  perspective  (as  in  Problem  XXIII).  Find 
the  eight  points  through  which  the  ellipse  representing  the  invisible  base 
is  to  be  drawn  by  carrying  lines  from  the  eight  points  already  found 
on  the  visible  base  to  V.  P.  R.,  and  projecting  to  them,  from  the  plan, 
the  corresponding  points  on  the  invisible  base.  Only  the  working  lines 
used  to  find  the  invisible  base  are  lined-in. 

The  entire  ellipse,  in  both  freehand  and  mechanical  perspective,  should 
always  be  drawn  even  if  but  a  small  part  of  its  circumference  is  after- 
wards lined-in.  In  no  other  way  can  the  true  elliptical  curve  be  ob- 
tained. 


10'  0" 


PROBLEM  XXV. 

Scale  }4"=1'0".  S.  P.  33'  0"  to  right  and  1'  0"  above.  C.  V. 
18'0"  from  S.  P.,  P.  L.  at  S.  P.,  H.  5'0"  above  S.  P. 

In  this  problem  a  plinth  16'0"  x  20'0"  and  3'0"  thick  rests  on  one 
3'  0"  x  20'  0"  face  and  vanishes  to  the  left  at  30°.  A  circular  arch 
is  cut  from  this  plinth  as  shown  by  the  elevation.  For  convenience  in 
working,  a  circle  of  the  size  of  the  arch  is  drawn  upon  the  picture  plane 
with  its  diameter  coinciding  with  the  nearest  vertical  edge  of  the  plinth. 

PROBLEM  XXVI. 

Scale  ^"=1'0.  S.  P.  6' 3"  to  right  and  6"  above.  C.  V.  8'  6" 
from  S.  P.,  P.  L.  1'  6"  from  S.  P.,  H.  4'  0"  above  P.  L. 

41 


SIMPLIFIED  MECHANICAL  PERSPECTIVE. 


XXVM 


t 


4- 


42 


THE  PERSPECTIVE  OF  CIRCLES. 

From  a  plinth  vanishing  to  the  right  at  45°,  base  5'0"  x  lO'O",  alti- 
tude 2'  0",  a  semi-circular  arch,  with  radius  of  4'  0",  is  cut  as  shown  by 
the  elevation.  From  the  drawing  it  will  be  seen  that  the  diagonals  of 
the  enclosing  square  may  be  put  into  perspective  and  used  as  tests  in  the 
location  of  the  eight  points  through  which  the  ellipse  is  drawn. 


PROBLEM  XXVII. 

Scale  %"=l'Q".  S.  P.  22'  0"  to  right  and  1'  0"  above.  C.  V. 
20'  0"  from  S.  P.,  P.  L.  2'  0"  above  S.  P.,  H.  10'  0"  above  P.  L. 

Any  area  may  be  put  into  perspective  by  enclosing  it  within  a  rec- 
tangle and  locating  points  in  its  perimeter  by  means  of  known  lines.  In 
this  problem  a  pointed-arch  opening,  as  a  door  or  window,  is  drawn. 
Lines  A  and  B  are  placed  at  random. 


43 


SIMPLIFIED  MECHANICAL  PERSPECTIVE. 


PROBLEM  XXVIII. 

It  is  hoped  that  students  have  noticed  that  while  the  short  diameters 
of  the  ellipses  drawn  have  coincided  with  a  diameter  or  diagonal  of  the 
square  used  in  finding  the  perspective  of  the  circles,  the  long  diameters 
have  not,  but  have  in  every  case  appeared  to  be  nearer  the  spectator.  In 


this  problem  the  method  of  finding  the  long  diameter  of  an  ellipse  repre- 
senting a  circle  upon,  or  parallel  to  the  horizontal  plane,  is  explained. 

In  practice  this  diameter  is  located  by  guess  as  an  ellipse  is  seldom 
drawn  large  enough  to  permit  the  exact  location  of  the  long  diameter 
to  be  found. 

Plate  vertical.  Scale  Y4"=\'  0".  S.  P.  16' 0"  to  right  and  TO" 
above.  C.  V.  15'  0"  from  S.  P.,  P.  L.  at  S.  P.,  H.  10'  0"  above  P.  L. 

The  circle  is  2V  0"  in  diameter. 

44 


THE  PERSPECTIVE  OF  CIRCLES. 

After  the  ellipse  is  found,  as  in  Problem  XXI,  draw  from  S.  P.,  to 
right  and  left,  lines  tangent  to  the  circle.  Find  the  exact  points  of  tan- 
gency  by  drawing  through  the  center  of  the  circle  lines  at  right  angles 
to  the  tangent  lines.  Points  X  and  Y  will  be  found  to  be  the  tangent 
points.  Put  X  and  Y  into  perspective,  according  to  Problem  V,  and 
the  ends  of  the  long  diameter  of  the  ellipse  will  be  found. 

PROBLEM  XXIX. 

Plate  vertical.  Scale  ^"=1'  0".  S.  P.  8' 0"  to  right  and  I'O" 
above.  C.  V.  9'  0"  from  S.  P.,  P.  L.  at  S.  P.,  H.  8'  0"  above  P.  L. 

In  this  problem  the  perspective  of  a  circular  plinth  (diameter  8'0", 
altitude  8'  0")  as  seen  by  an  eye  9'  0"  distant  and  8'  0"  above  the  hori- 
zontal plane  is  found.  Any  object  so  large,  seen  from  so  near,  will  ap- 
pear when  put  into  perspective,  as  distorted  or  in  "violent  perspective," 
as  Problem  XXIV,  but  from  this  problem  two  facts  relating  to  the  ap- 
pearance of  cylindrical  objects  of  great  assistance  in  freehand  drawing 
can  be  learned: 

First:  The  short  diameter  of  the  farther  ellipse  is,  compared  with 
the  long  diameter,  proportionately  greater  or  longer  than  the  short  diam- 
eter of  the  nearer  ellipse. 

Second:  The  long  diameters  of  the  ellipses  representing  the  bases 
are  at  right  angles  to  the  axis  of  the  solid.  This  is  but  approximately 
true  in  this  problem  on  account  of  its  violent  perspective,  but  is  near 
enough  to  enable  the  student  to  realize  that  tests  for  the  drawings  of 
cylindrical  objects  are  lines  drawn  to  represent  the  axes  of  the  objects 
and  lines  at  right  angles  to  the  axes  to  represent  the  long  diameters  of 
the  ellipses. 

If  the  point  of  intersection  of  the  long  diameter  of  an  ellipse  repre- 
senting the  circular  base  with  the  axis  of  an  object  should  be  taken  as 
C.  V.  there  would  be  no  distortion  and  the  right  angle  would  appear 
as  such. 


45 


SIMPLIFIED   MECHANICAL   PERSPECTIVE. 


UV.PL 


THE  PERSPECTIVE  OF  OBLIQUE  LINES. 

SO  FAR,  in  this  course  in  perspective,  we  have  found  and  used  only 
the  vanishing  points  of  retreating  horizontal  lines  all  of  which 
have  been  found  in  the  horizon. 

It  is  now  time  to  use  the  vanishing  points  of  oblique  lines,  for  all 
lines,  whatever  their  direction,  that  are  not  parallel  to  the  picture  plane, 

have  vanishing  points. 

In  Fig.   14,  not  only  do  lines 
1-4,  3-5  and  2-6  vanish  at  V.  P. 
R.,  and  lines  1-2  and  4-6  at  V.  P. 
L.,  but  lines   1-3   and  4-5,  which 
are  parallel,  vanish  at  U.  V.  P.  L. 
(Upper    Vanishing    Point    Left.) 
and  lines  3-2  and  5-6  at  L.  V.  P. 
v/p-p   L.  (Lower  Vanishing  Point  Left.) 
If  these  upper  and  lower  van- 
ishing points  can  be  found  in  ad- 
vance, as  V.  P.  R.  and  V.  P.  L. 
are  found,  their  use  will  make  the 
solving  of  many  problems  much  easier  and  simpler. 
Line    1-2,    Fig.    14,    is   a  retreating   horizontal 
line,  and  1-3  a 
retreating    ob- 
lique line,  but 
they    both    lie 

in  the  same  vertical  plane.  Planes 
have  their  vanishing  traces  as  lines 
have  their  vanishing  points.  H  is 
the  vanishing  trace  of  all  horizon- 
tal planes.  A  vertical  drawn  thru 
V.  P.  L.  is  the  vanishing  trace  of 
the  vertical  plane  of  which  the  tri- 
angle 1-2-3  forms  a  part.  All  lines 
lying  in  or  parallel  to  a  plane  have 
their  vanishing  points  in  the  van- 


..1VRL 


uKjd  si|j  jo 
the  vanishing  point  of  4-5,  as  well  as  that  of  1-3,  must  be  in  this  vertical 


46 


TTo.16. 


THE  PERSPECTIVE  OF  OBLIQUE  LINES. 

trace  above  V.  P.  L.  and  the  vanishing  point  of  3-2  and  5-6  must  be 
below  V.  P.  L. 

If  the  vertical  plane  containing  triangle  1-2-3  be  revolved  to  co- 
incide with  the  V.  PI.  the  true  angle  made  with  the  horizontal  plane  by 
1-3  may  be  seen  and  the  vanishing 
point  of  1-3,  and  all  lines  parallel 
to  1-3,  found.  It  is  known  that  the 
vertical  plane  containing  1-2-3 
makes  an  angle  to  the  left  of  45°, 
therefore,  Fig.  15,  line  X-S.  P.  is 
revolved  to  Tr.  V.  PL  and  the  an- 
gle made  by  1-3  with  the  horizon- 
tal plane  (in  this  case  45°)  is  con- 
structed and  point  A  found.  If  Tr. 
V.  PL  was  used  as  the  horizon 
point,  A  would  be  the  vanishing 
point  of  all  lines  making  angles  of 


Tr.V.71. 


H. 


EL, 


A 


45°   to  the  left  with  the  vertical 

plane  and   angles  of  45°   upward 

with   the  horizontal   plane. 

As  has  been  explained  (Plate  I)  Tr.  V.  PL  is  not  used  as  the  horizon, 

point  to  be  used  as  the  U.  V.  P.  L. 
( B )  is  placed  as  far  above  H.  as  A 
is  above  Tr.  V.  PL  That  is,  dis- 

^  i.  tance   C-B   is  made  equal   to   dis- 

tance X-A. 

A  diagram  for  a  problem  con- 
taining lines  vanishing  to  right  or 
on  acount  of  the  confusion  of 
lines,  but  a  new  line  (H)  is  drawn 
the  required  distance  above  P.  L. 
which  is  placed  wherever  con- 
venient. 

As  A,  Fig.  16,  is  found  to  be 
distance  X-A  from  Tr.  V.  PL,  the 


B 
LVPL< 


V.-RR. 


I! 


im 


left  at  45°  with  the  vertical  plane  and  up  or  down  at  45°  with  the  hori- 
zontal plane  is  constructed  as  in  Fig.  17.  Distance  V.  P.  L.  —  U.  V.  P. 
L.  is  made  equal  to  distance  X-A.  Distance  V.  P.  L.  —  L.  V.  P.  L.  is 
made  equal  to  distance  X-B.  Distance  V.  P.  R.  —  U.  V.  P.  R.  is  made 


47 


SIMPLIFIED   MECHANICAL  PERSPECTIVE. 


48 


THE  PERSPECTIVE  OF  OBLIQUE  LINES. 

equal  to  distance  Y-C.    Distance  V.  P.  R.  —  L.  V.  P.  R.  is  made  equal 

to  distance  Y-D. 

In  Fig.  14,  line  1-2  is  included  in  two  planes.     It  is  in  a  horizontal 

plane  and  also  in  a  vertical  plane.     Its  vanishing  point  is  V.  P.  L.  the 

point  of  intersection  of  the  traces  of  the  two  plances  containing  the  line. 

Every  retreating  line  lying  in 
two  planes  has  its  vanishing  point 
at  the  intersection  of  the  traces  of 
the  planes. 

In  Fig.  18,  U.  V.  P.  L.  —  V. 
P.  R.  is  the  vanishing  trace  of  the 
plane  containing  1-2-4-3,  and  U. 
V.  P.  R.— V.  P.  L.  is  the  vanish- 
ing trace  of  the  plane  containing 
1-5-6.  Therefore  line  1-6,  which  is 
common  to  both  planes,  will  have 

its  vanishing  point  at  X,  the  point  of  intersection  of  the  traces  of  the 

two  planes  containing  the  line. 

PROBLEM  XXX. 

Plate  vertical.  Scale  %"=1'  0".  S.  P.  16'  0"  to  right  and  IT  0" 
above.  C.  V.  13'0"  from  S.  P.,  P.  L.  at  S.  P.,  H.  8'0"  above  P.  L. 

In  this  problem  a  square  13"  0"  x  13'0"  rests  on  an  edge  that  van- 
ishes to  the  right  at  45°.  The  square  makes  an  angle  of  45°  with  the 
horizontal  plane.  The  square  does  not,  of  course,  appear  as  such  in  the 
plan.  V.  P.  R.  is  the  vanishing  point  of  the  two  edges  parallel  to  the 
horizontal  plane.  U.  V.  P.  L.  is  the  vanishing  point  of  the  two  edges 
making  angles  of  45°  upward  to  the  left. 

In  laying  out  the  diagram  for  a  problem  containing  lines  making 
angles  with  both  the  horizontal  and  vertical  planes  it  is  always  advisable 
to  find  the  four  upper  and  lower  vanishing  points  that  their  location 
may  be  known  before  the  problem  is  worked. 

PROBLEM  XXXI. 

Scale  ^"=1'0".  S.  P.  8'0"  to  right  and  5'  6"  above.  C.  V. 
6' 6"  from  S.  P.,  P.  L.  at  S.  P.,  H.  4'  0"  above  P.  L. 

A  box  4'0"  x  6'  0"  and  3'  0"  deep  stands  on  the  horizontal  plane 
as  shown  by  the  plan.  The  cover  is  open  at  an  angle  of  30°. 


49 


SIMPLIFIED  MECHANICAL  PERSPECTIVE. 

PROBLEM  XXXII. 

Scale  #"=1'0".     S.  P.  32' 0"  to  right  and  22'  0"  above.     C.  V. 
26'  0"  from  S.  P.,  P.  L.  at  S.  P.,  H.  16'  0"  above  P.  L. 

A  triangular  prism,  size  and  location  shown  by  plan  and  elevation, 
is  drawn  using  upper  and  lower  vanishing  points. 


PROBLEM  XXXIII. 

Scale  J4"=1'0".  S.  P.  16' 0"  to  right  and  11' 0"  above.  C.  V. 
13'  0"  from  S.  P.,  P.  L.  at  S.  P.,  H.  8'  0"  above  P.  L. 

A  cube,  faces  8'  0"  x  8'  0",  rests  on  one  edge  as  shown  by  the  plan 
and  elevation.  All  lines  used  to  obtain  the  perspective  are  lined-in  to 
show  how  few  are  necessary  to  work  the  problem. 


50 


THE  PERSPECTIVE  OF  OBLIQUE  LINES. 


X 
X 
X 


51 


SIMPLIFIED  MECHANICAL  PERSPECTIVE. 


52 


THE  PERSPECTU'E  OF  OBLIQUE  LINES. 


PROBLEM  XXXIV. 

Scale  J4"=1'0".  S.  P.  12' 0"  to  right  and  6' 0"  above.  C.  V. 
lO'O"  from  S.  P.,  P.  L.  at  S.  P.,  H.  5'  0"  above  P.  L. 

A  cube,  faces  7'  0"  x  7'  0",  rests  on  one  edge  as  shown  by  the  plan 
and  elevation.  First  find  the  perspective  of  the  edge  of  the  cube  resting 
in  the  horizontal  plane. 

PROBLEM  XXXV. 

Scale  #"=1'0".  S.  P.  32'  0"  to  right  and  22'  0"  above.  C.  V. 
26'  0"  from  S.  P.,  P.  L.  at  S.  P.,  H.  16'  0"  above  P.  L. 


XXXVII 


This  is  a  problem  that  frequently  presents  itself  when  drawing 
roofs.  All  dimensions  necessary  for  working  the  problem  are  given  on 
the  plan  and  elevation.  The  intersection  of  the  roof  vanishes  at  the 
intersection  of  the  traces  of  the  roofs  as  explained  in  Fig.  18.  It  is  as 

53 


THE  PERSPECTIVE  OF  OBLIQUE  LINES. 

necessary  for  a  draftsman  making  a  freehand  drawing  of  roofs  to  know 
where  the  line  of  intersection  vanishes  as  it  is  for  the  architect  who  is 
drawing  a  perspective  mechanically. 


PROBLEM  XXXVI. 

Scale  i4"=l'0".  S.  P.  16'  0"  to  right  and  11' 0"  above.  C.  V. 
13' 0"  from  S.  P.,  P.  L.  at  S.  P.,  H.  8'  0"  above  P.  L. 

In  this  problem  a  chimney,  4'  0"  x  4' 0",  extends  from  the  center  of 
a  roof  16'0"  x  16'0".  The  top  of  the  chimney  is  12'0"  from  the  hori- 
zontal plane. 

PROBLEM  XXXVII. 

Scale  j/S"=l' 0".  S.  P.  32'  0"  to  right  and  22'  0"  above.  C.  V. 
26'  0"  from  S.  P.,  P.  L.  at  S.  P.,  H.  16'  0"  above  P.  L. 

In  this  problem  a  dormer-window  extends  from  a  roof  28' 0"  x 
30'  0".  Other  dimensions  necessary  for  the  working  of  this  problem 
are  given  on  the  elevations. 


54 


Books    on    the    Manual   Arts 


Essentials  of  Woodworking.     By  IRA  s.  GRIFFITH;  illustrated 
with  numerous  pen  drawings  by  Edwin  V.  Lawrence. 

This  is  a  comprehensive  textbook  on  woodworking  tools,  materials  and  processes,  to  supplement, 
but  not  to  take  the  place  of,  the  instruction  given  by  the  teacher.  The  book  contains  three  parts: 
I  —  Tools  and  elementary  processes,  including  laying-out  tools  and  their  use,  saws,  planes  and 
their  use,  boring  tools,  chisels,  grinding  and  whetting,  form  work,  laying  out  duplicate  parts, 
scraping,  sandpapering,  and  fastening  parts.  II  —  Simple,  joinery,  including  directions  for  making 
the  common  joints,  elementary  cabinet  work  involving  drawer  construction,  paneling,  rabbeting, 
and  door  construction.  Ill  —  Wood  and  wood-finishing,  including  a  great  amount  of  information 
that  should  be  given  to  a  student  along  with  his  work  in  wood.  The  book  does  not  contain  a  course  ' 
of  models.  It  may  be  used  with  any  course.  Price.  $1.00. 

Beginning  Woodwork.    At  Home  and  in  School.    By  CLINTON 
SHELDON  VAN  DEUSEN;  illustrated  by  Edwin  Victor  Lawrence. 

A  full  and  clear  description  in  detail  of  the  fundamental  processes  of  elementary  benchwork 
in  wood.  This  description  is  given  through  directions  for  making  a  few  simple,  useful  articles 
suitable  either  for  school  or  home  problems.  Even  without  a  teacher  a  bright  boy,  by  following 
this  book  faithfully,  may  acquire  considerable  skill.  It  is  a  safe  guide  for  farmers'  boys  as  well  as 
for  city  boys,  and  is  especially  well  suited  for  use  in  rural  and  village  schools  in  which  the  teacher 
has  had  but  little  experience  in  the  use  of  woodworking  tools.  The  book  is  illustrated  by  more 
than  one  hundred  figures,  including  ten  plates  cf  working  drawings.  Each  of  these  figures  is  an 
original  drawing  made  expressly  for  this  book.  Price.  $1.00. 

Problems  in  Woodworking.     By  M.  w.  MURRAY. 

A  convenient  collection  of  good  problems  ready  to  place  in  the  hands  of  the  pupils.  It  consists  of 
forty  plates  bound  in  heavy  paper  covers  with  brass  fasteners.  Each  plate  is  a  working  drawing,  or 
problem  in  bench  work  that  has  been  successfully  worked  out  by  boys  in  one  of  the  grades  from 
seven  to  nine  inclusive.  Many  of  the  problems  can  be  worked  out  in  various  ways  according  to 
the  individual  ability,  interest  and  taste  of  the  puvil.  Price,  75  cents.  Board  covers,  20  cents  extra. 


Problems  in  Furniture  Making.     By  FRED  D.  CRAWSHAW. 

This  book  consists  of  32  plates  of  working  drawings  suitable  for  use  in  grammar  and  high  schools 
and  24  pages  of  text,  including  chapters  on  design,  construction  and  finishes,  and  notes  on  the 
problems.  Price,  in  heavy  paper  covers,  $1.00.  Board  covers.  20  cents  extra 


Problems  in  Mechanical  Drawing.      By  CHARLES  A.   BEN- 
NETT.    With  drawings  made  by  Fred  D.  Crawshaw. 

This  book  consists  of  80  plates  and  a  few  explanatory  notes,  and  is  bound  in  heavy  paper  covers 
with  brass  fasteners.  Its  purpose  is  to  furnish  teachers  of  classes  beginning  mechanical  drawing 
with  a  large  number  of  simple,  practical  problems.  These  have  been  selected  with  reference  to  the 
formation  of  good  habits  in  technique,  the  interest  of  the  pupils,  and  the  subjects  usually  included 
in  a  grammar  and  first-year  high  school  course.  The  book  covers  simple  projection — straight 
lines  and  circles,  problems  involving  tangents,  planes  of  projection,  revolution  of  solids,  develop- 
ments, intersections,  isometric  projection,  lettering  and  working  drawings.  Each  problem  given 
is  unsolved  and  therefore  in  proper  form  to  hand  to  the  pupil  for  solution.  Price,  $1.00.  Board 
covers,  20  cents  extra. 


Woodwork  for  Schools  on  Scientific  Lines.     By  JAMES 

THOMAS    BAILY   and   S.  POLLITT. 

This  is  the  American  edition  of  an  English  book  containing  many  problems  designed  to  cor- 
relate mathematics  and  physical  science  with  manual  training.  Price,  75  cents. 

Clay  Work.     By  KATHERINE  MORRIS  LESTER. 

This  book  covers  the  whole  range  of  clay  work  for  the  elementary  school — technique  of  clay 
modeling,  study  of  plant  forms,  human  figure,  story  illustration,  simple  architectural  ornament,  the 
making  of  tiles  and  ornamental  pottery.  Price,  $1.00. 

Classroom  Practice  in  Design.    By  JAMES  PARTON  HANEY. 

A  concise,  up-to-date,  richly  illustrated  booklet  on  the  teaching  of  applied  design.  Very  sug- 
jresthe.  Price,  50  cents. 

The  Wash  Method  of  Handling  Water  Colour.    By  FRANK 

FOKRKST    FKKDKRICK. 

"This  little  book  is  a  helpful  guide  and  affords  a  stimulus  to  the  use  of  water-color  as  practiced 
by  the  earlier  painters,  whose  beautiful  work  is  unexcelled."  Price,  50  cents. 

Manual  Training  Magazine. 

An  illustrated,  bi-monthly  publication  devoted  to  the  interests  of  the  Manual  Arts  in  Education. 
Subscription  price,  $1.50  a  vear:  single  copies,  35  cents.  In  foreign  countries,  including  Canada, 
$1.75  a  vear:  single  copies,  40  cents. 


The    Manual    Arts    Press 

Peoria,     Illinois 


UC  SOUTHERN  REGIONAL  LIBRARY  FACILITY 


A     000  085  439     8 


